1. Field of the Invention
The invention relates to a rectangular brilliant-cut of a diamond provided with a new facet configuration. The rectangular brilliant-cut is sometimes referred to as the princess cut.
2. Description of the Related Art
The size of an ornamental cut diamond depends on the size of the raw stone. In particular, the crown height, pavilion depth and girdle size are determined by the size of the raw stone.
Even if the size of a diamond is the same, the brilliancy of the diamond is varied by its cut. The present inventors have introduced, for a round brilliant cut diamond, the concept of xe2x80x9cvisual-perceptible reflection rays,xe2x80x9d and on the basis thereof have invented a cut design which can increase the visual-perceptible reflection ray amount for the purpose of evaluating the brilliancy that can be perceived by an observer when a diamond is observed; and the patent application thereof has been made (Japanese Patent Application No. 2002-253011 filed Aug. 30, 2002 and its counterpart foreign Patent Applications, e.g., for the US, U.S. Ser. No. 10/350,388, filed Jan. 23, 2003).
In the previous patent application of the round brilliant cut diamond, the amount of physical reflection rays was obtained in such a manner that meshes are defined by dividing the radius of the diamond into 100 equal segments and the ray density was obtained with respect to each mesh. Since the radius of diamonds is several millimeters, a mesh area is several hundred square micrometers. The amount of light was calculated only with respect to patterns of 30 meshes or larger by considering the area perceptible by human eyes. Amounts of visual-perceptible reflection rays were defined to be the square root of values of tenths of the amount of physical reflection rays with respect to all the patterns, and the sum of the amounts of visual-perceptible reflection rays was obtained with respect to all the patterns. That is, the amount of visual-perceptible reflection rays was calculated by the following equation:
The amount of visual-perceptible reflection rays=xcexa3{(the amount of physical reflection rays with respect to patterns of 30 meshes or larger in each segment)/10}1/2, in which xcexa3 is the sum of patterns in one segment.
When a diamond is observed by an observer above the table of the diamond, the light rays incident from the backside of the observer are blocked by the observer and hence do not reach the diamond. On the contrary, the light rays with large incident angles do not effectively contribute to the reflection. Accordingly, by assuming that the light rays with the incident angles of 20 to 45 degrees with respect to the normal to the table facet of the diamond (namely, the center line connecting the table facet center and the culet) are effective light rays, the intensity of the reflection derived from the above described range of incident light rays is referred to as xe2x80x9cthe effective visual-perceptible reflection ray amount,xe2x80x9d and a cut design capable of increasing the effective visual-perceptible reflection ray amount has also been investigated in the above described patent application.
In the study of the reflection rays from the diamond, the above described effective visual-perceptible reflection ray amount is effective when uniform light rays are incident from around all the surrounding portions; on the other hand, when the light is irradiated from a plane ceiling, it is necessary that the light intensity is represented by cos2 xcex8 where xcex8 is the incident angle.
In the rectangular brilliant-cut, there are formed a rectangular columnar girdle between a rectangular upper cross section and a rectangular lower cross section parallel thereto, a crown above the girdle, and a pavilion below the girdle. Because a rectangular brilliant-cut with a square girdle is often used, description will be made below assuming that a square cross section is provided.
As FIG. 16 shows the top view, FIG. 17 shows the side view and FIG. 18 shows the bottom view, the conventional rectangular brilliant-cut 400 has a square truncated pyramid shape crown 420 above a rectangular columnar girdle 410 having a square cross section and a square pyramid shape pavilion 440 below the girdle 410. In these figures, the respective x, y and z axes are shown on the basis of a coordinate system having its origin at the center of a horizontal cross section bbxe2x80x2bbxe2x80x2 formed with four vertexes in the underpart of the girdle 410. The center line connecting the table facet center and the culet R is taken as the z axis, and the horizontal cross section bbxe2x80x2bbxe2x80x2 is taken as the xy plane. The square truncated pyramid shape crown 420 has on the surface thereof the table facet 421, four bezel facets 423, four crown girdle facets 427, four second bezel facets 429, and eight star facets 431. The table facet 421 is situated on a plane parallel to the xy plane. The table facet 421 is the top plane of the truncated pyramid shape crown 420; in which four first vertexes F,Fxe2x80x2 are respectively provided near the upper vertexes B, Bxe2x80x2 of the square girdle 410, and four second vertexes Del each is located at a point displaced outwardly from the midpoint of a line segment, connecting two neighboring first vertexes F, Fxe2x80x2 of the four first vertexes, along the line connecting the table center and the midpoint; thus, the table facet 421 is an octagon formed by connecting each of the four second vertexes Del with the adjacent pair of the four first vertexes F, Fxe2x80x2 respectively in one-to-one correspondence with the four vertexes B, Bxe2x80x2 of the girdle. A bezel facet 423 is a quadrilateral BCFD in which a pair of diagonal vertexes are the pair of a vertex B and a vertex F or the pair of a vertex Bxe2x80x2 and a vertex Fxe2x80x2 where the vertexes B and Bxe2x80x2 are the upper vertexes of the girdle 410 and the vertexes F and Fxe2x80x2 are respectively in one-to-one correspondence with the vertexes B and Bxe2x80x2. Each crown girdle facet 427 is a trapezoid BBxe2x80x2CCxe2x80x2 which is formed with a side (for example, BBxe2x80x2) of the upper cross section of the girdle 410 and the sides BC and Bxe2x80x2Cxe2x80x2, closest to the above described girdle edge BBxe2x80x2, among the sides in the two bezel facets 423 each having as a vertex thereof any of the two ends B and Bxe2x80x2 of the side BBxe2x80x2. A second bezel facet 429 is a triangle CCxe2x80x2Del which is formed with the side CCxe2x80x2, parallel to and opposite to the girdle edge BBxe2x80x2 among the sides of the crown girdle facet 427, and a second vertex Del, opposite to the midpoint of the side BBxe2x80x2 of the girdle facet 427, among the vertexes of the table facet 421. A star facet 431 is a triangle CFDel which is enclosed with a side FDel of the table facet 421, a side CF of a bezel facet 423 and a side CDel of the second bezel facet 429.
A square pyramid shape pavilion 440 has on the external surface thereof four pavilion main facets 441, four pavilion girdle facets 443, and a plurality of facets 447, 449 and 451 dividing a portion between a pavilion main facet 441 and the pavilion girdle facet 443. Each of the pavilion main facets 441 is a quadrilateral bLRLxe2x80x2 in which a vertex b in the lower portion of the girdle and the lower apex (culet) R of the square pyramid shape pavilion 440 are a pair of diagonal vertexes. The straight line passing through the lower apex R of the square pyramid shape pavilion 440 and the table facet center will be referred to as the xe2x80x9ccenter linexe2x80x9d (the z axis), and the plane including the center line and dividing an edge of the square girdle at the midpoint thereof will be referred to as the xe2x80x9ccenter dividing planexe2x80x9d (the zx or yz plane). Every pavilion facet 441 has the vertexes L and Lxe2x80x2, opposing each other, on the center dividing planes, and a pair of adjacent pavilion facets share the side LR connecting the vertex L on the center dividing plane intervening the pair of facets and the lower apex R. Every pavilion girdle facet 443 is a triangle bbxe2x80x2S formed with a side bbxe2x80x2 of the lower cross section of the girdle and a point S located on the center dividing plane intersecting the side bbxe2x80x2. A pavilion main facet 441 (bLRLxe2x80x2) and a pavilion girdle facet 443 (bbxe2x80x2S) share a vertex of the girdle. Two boundary lines bM and bN are provided between the side bL passing through the vertex b of the lower cross section of the girdle among the sides of a pavilion main facet 441 and the side bS of a pavilion girdle facet 443 passing though the same vertex b of the girdle, having their ends on the center dividing plane common to the vertex L; thus, owing to these two boundary lines, three triangles 447, 449, 451 are provided between the two facets 441 and 443, the three triangles sharing the vertex shared by these two facets 441, 443.
As for the rectangular brilliant-cut, a cut capable of enlarging the visual-perceptible reflection ray amount has been investigated. Thus, it has been found that in the rectangular brilliant-cut, once the crown height, the pavilion depth and the girdle size have been specified, the sizes of the table facet and star facets are fixed so that it is impossible to enlarge the visual-perceptible reflection ray amount through selecting an optimal crown angle. The variation of the crown height may lead to the alteration of the sizes of the table facet and star facets, but the possibility of the crown height variation is dependent on the size of the raw stone. Now, the following fact has been revealed: the reduction in size of the table facet and enlargement in size of the star facets, for the purpose of enlarging the visual-perceptible reflection ray amount, inevitably leads to the increase of the table facet height; thus, the angle formed by a second bezel facet and the table facet or the horizontal cross section (the xy plane) formed by the upper or lower four vertexes of the girdle becomes larger than the crown angle formed by a crown girdle facet present on a side of the upper cross section of the girdle and the table facet or the horizontal cross section (the xy plane) formed by the upper or lower four vertexes of the girdle so that the cut becomes impossible actually.
Thus, an object of the invention is to provide a rectangular brilliant-cut diamond improved so as to be provided with a facet configuration capable of having an optimal shape for the purpose of enlarging the visual-perceptible reflection ray amount.
Additionally, another object of the invention is to provide a cut design based on the above described facet configuration and optimal for the purpose of enlarging the visual-perceptible reflection ray amount.
According to the invention, an improved rectangular brilliant-cut diamond comprises a rectangular columnar girdle, a crown having an octagonal table facet on a top of the crown and formed above the girdle and a pavilion below the girdle. The rectangular columnar girdle has an upper rectangular cross section parallel to the table facet at a boundary between the girdle and the crown. The crown comprises four trapezoidal crown girdle facets or upper girdle facets, four lower triangular bezel facets, four upper triangular bezel facets, four second triangular bezel facets and eight triangular star facets on an outer surrounding surface of the crown. The table facet has four first vertexes and four second vertexes, each of the four first vertexes being located adjacent to each of four vertexes of the upper cross section of the girdle and each of the four second vertexes being at a point displaced in a direction opposite to a line (hereinafter referred to as xe2x80x9ccenter linexe2x80x9d) vertical to the table facet from a center point between the two neighboring first vertexes. The four crown girdle facets and the four lower bezel facets are aligned alternately to form a row along and above the boundary. Each of the four crown girdle facets has a base coinciding with a side of the upper cross section of the girdle and each of the lower bezel facets has a vertex, two sides passing the vertex and a base opposite to the vertex, the vertex coinciding with each of the vertexes of the upper cross section of the girdle and jointly owned by two crown girdle facets on both sides of each of the lower bezel facets, the two sides each coinciding with a side of each of the two crown girdle facets and the base having two ends each coinciding with a vertex owned by each of the two crown girdle facets. The four upper bezel facets, the four second bezel facets and the eight star facets are aligned to form another row between the table facet and the row having the crown girdle facets and the lower bezel facets. Each of the upper bezel facets has a vertex coinciding with one of the first vertexes of the table facet and a base coinciding with the base of the lower bezel facets. Each of the lower bezel facets has an angle with the table facet larger than an angle between each of the upper bezel facets and the table facet.
The pavilion comprises four rectangular pavilion main facets and a plurality of triangular pavilion girdle facets or lower girdle facets on an outer surrounding surface of the pavilion. Each of the pavilion main facets has two opposite vertexes, one of which is a lower apex of the diamond on the center line and the other of which coincides with each of lower vertexes of the girdle, and two sides each coinciding with a side owned by a neighboring pavilion main facet on a plane (hereinafter referred to as xe2x80x9ccenter dividing planexe2x80x9d) passing both the center line and a center between two neighboring lower vertexes of the girdle.
In the improved rectangular brilliant-cut diamond of the invention, the pavilion may comprise four triangular pavilion girdle facets. Each of the pavilion girdle facets has a base coinciding with a connecting line between the two neighboring lower vertexes of the girdle and a vertex opposite to the base on the center dividing plane crossing the base. One of the pavilion main facets and a pavilion girdle facet adjacent to the pavilion main facet jointly own a vertex coinciding with one of the lower vertexes of the girdle, the pavilion main facet has a side passing the co-owned vertex and an end on the same center dividing plane, and the pavilion girdle facet adjacent to the pavilion main facet has a side passing the co-owned vertex and another end on the same center dividing plane. Between the side of the pavilion main facet and the side of the pavilion girdle facet adjacent to the pavilion main facet, the pavilion has at least two triangular facets, owning the co-owned vertex, divided into by at least one neighboring boundary line passing the co-owned vertex and an end on the same center dividing plane. Between the side of the pavilion main facet and the side of the pavilion girdle facet, the pavilion may have one to four boundary lines, by which there are two to five triangular facets divided into.
In the improved rectangular brilliant-cut diamond of the invention, the pavilion may comprise eight triangular pavilion girdle facets. Each of the pavilion girdle facets has a vertex on a crossing line between a girdle side facet and a center dividing plane crossing the girdle side facet, another vertex coinciding with a lower vertex of the girdle side facet, and a separated vertex on the center dividing plane. Each of the pavilion girdle facets has a side co-owned on the center dividing plane with a neighboring pavilion girdle facet that has a vertex coinciding with another lower vertex of the same girdle side facet. The two neighboring pavilion girdle facets have such an angle between them that the co-owned side on the center dividing plane forms a ridge between them. One of the pavilion main facets and a pavilion girdle facet adjacent to the pavilion main facet jointly own a vertex coinciding with one of the lower vertexes of the girdle. The pavilion main facet has a side passing the co-owned vertex and an end on the same center dividing plane, and the pavilion girdle facet adjacent to the pavilion main facet has a side passing the co-owned vertex and another end on the same center dividing plane. Between the side of the pavilion main facet and the side of the pavilion girdle facet adjacent to the pavilion main facet, the pavilion has at least two triangular facets, owning the co-owned vertex, divided into by at least one neighboring boundary line passing the co-owned vertex and further another end on the same center dividing plane. Between the side of the pavilion main facet and the side of the pavilion girdle facet, the pavilion may have one to four boundary lines, by which there are two to five triangular facets divided into.
In the improved rectangular brilliant-cut diamond of the invention, it is preferable that the pavilion has one boundary line passing the co-owned vertex of the girdle and the other end on the same center dividing plane to have two triangular facets, owning the co-owned vertex, divided into by the neighboring boundary line between the side of the pavilion main facet and the side of the pavilion girdle facet adjacent to the pavilion main facet.
In the improved rectangular brilliant-cut diamond of the invention, it is preferable that the angle between the lower bezel facet and the table facet is 23 to 26 degrees, that the angle between the upper bezel facet and the table facet is smaller than the angle between the lower bezel facet and the table facet and 13 to 25 degrees, and that the pavilion main facet is at an angle of 38 to 42 degrees with the table facet.
In the improved rectangular brilliant-cut diamond of the invention, assuming that the center line stands at the origin (0, 0) of x, y-coordinates and that one of the girdle lower vertexes is at (2, 2) of the x, y-coordinates, it is preferable that the first vertex, adjacent to the girdle lower vertex, of the table facet is at (0.7 to 1.2, 0.7 to 1.2) of the x, y-coordinates, that the three lines closest to the center line among the side of the pavilion main facet, the side of the pavilion girdle facet, and the boundary lines between the side of the pavilion main facet and the side of the pavilion girdle facet adjacent to the pavilion main facet cross the center dividing plane at points closer to the origin than x-coordinate of the first vertex of the table facet, and that the second vertex of the table facet is at x-coordinate of 1.3 to 1.6.